black  In order to implement this proposal, we consider metallic nanosphere as a core of radius \(b\)  embedded in dielectric spherical shell of radius \(a,\)  forming a core-shell nanoparticle [1]}, [2]}, [3]}, [4]}. Assuming that the core is silver (\(\rm Ag\) ) and we may use Drude formula to define it's permittivity, \(\epsilon _c=\epsilon _\infty -\frac{\omega ^2_p}{\omega (\omega +i\Gamma )}\) , with \(\omega _p = 9.2 eV,\)  \( \Gamma = 0.0212\, eV,\)  \( \epsilon _\infty = 5.0,\)  where \(1 eV = 241.8\, THz \)  [5]} and \(\omega \)  is the angular frequency of incident light. Furthermore, the core-shell is homogenized to an effective sphere of radius \(a\)  with permittivity \(\epsilon _{\rm MG}\)  provided by Eq. (REF ) and displayed in Fig. REF (b) at fixed radii ratio at \(\frac{b}{a} =0.84\) . It has been verified that in the quasi-static limit, the effective sphere has a good agreement to exact Mie solution of a core-shell nanoparticles of the same dimension [6]} and indeed it can be used as inclusion into a host medium to fabricate the structures of desired optical and physical properties [7]}, [6]}, [9]}, [10]}.
